The Self-energy of Nucleon for the Pion-nucleon Scattering Parameter

TL;DR

This paper calculates the pion-nucleon scattering amplitude considering both perturbative and non-perturbative effects, highlighting the significant role of sigma-meson mediation in the process.

Contribution

It introduces a lowest-order perturbative approach combined with non-perturbative terms to determine nucleon self-energy and scattering parameters.

Findings

Sigma-meson mediation is crucial in pion-nucleon scattering.

The approach successfully reproduces S-wave scattering parameters.

Pseudovector pion interaction significantly influences the scattering process.

Abstract

The scattering amplitude of the pion-nucleon elastic scattering is calculated by the lowest-order approximation of the perturbative expansion with the non-perturbative term. The self-energy of nucleon is determined so as to give the scattering parameters of the $S$-wave. It is shown that the scattering process mediated by the $\sigma$-meson plays a decisive role together with the pseudovector pion interaction.